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Fast Optimal Three View Triangulation

Byröd, Martin LU ; Josephson, Klas LU and Åström, Karl LU (2008) Swedish Symposium on Image Analysis (SSBA) 2008 p.95-98
Abstract
We consider the problem of L2-optimal triangulation from three separate views. Triangulation is an important part of numerous computer vision systems. Under gaussian noise, minimizing the L2 norm of the reprojection error gives a statistically optimal estimate. This has been solved for two views. However, for three or more views, it is not clear how this should be done. A previously proposed, but computationally impractical, method draws on Gröbner basis techniques to solve for the complete set of stationary points of the cost function. We show how this method can be modified to become significantly more stable and hence given a fast implementation in standard IEEE double precision. We evaluate the precision and speed of the new method on... (More)
We consider the problem of L2-optimal triangulation from three separate views. Triangulation is an important part of numerous computer vision systems. Under gaussian noise, minimizing the L2 norm of the reprojection error gives a statistically optimal estimate. This has been solved for two views. However, for three or more views, it is not clear how this should be done. A previously proposed, but computationally impractical, method draws on Gröbner basis techniques to solve for the complete set of stationary points of the cost function. We show how this method can be modified to become significantly more stable and hence given a fast implementation in standard IEEE double precision. We evaluate the precision and speed of the new method on both synthetic and real data. The algorithm has been implemented in a freely available software package which can be downloaded from the Internet. (Less)
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Contribution to conference
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published
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pages
4 pages
conference name
Swedish Symposium on Image Analysis (SSBA) 2008
language
English
LU publication?
yes
id
7c6256b7-82ce-4b76-81ad-757167f964b1 (old id 1050640)
alternative location
http://www.maths.lth.se/vision/publications/publications/view_paper.php?paper_id=400
date added to LUP
2008-07-01 12:10:27
date last changed
2016-08-31 14:56:14
@misc{7c6256b7-82ce-4b76-81ad-757167f964b1,
  abstract     = {We consider the problem of L2-optimal triangulation from three separate views. Triangulation is an important part of numerous computer vision systems. Under gaussian noise, minimizing the L2 norm of the reprojection error gives a statistically optimal estimate. This has been solved for two views. However, for three or more views, it is not clear how this should be done. A previously proposed, but computationally impractical, method draws on Gröbner basis techniques to solve for the complete set of stationary points of the cost function. We show how this method can be modified to become significantly more stable and hence given a fast implementation in standard IEEE double precision. We evaluate the precision and speed of the new method on both synthetic and real data. The algorithm has been implemented in a freely available software package which can be downloaded from the Internet.},
  author       = {Byröd, Martin and Josephson, Klas and Åström, Karl},
  language     = {eng},
  pages        = {95--98},
  title        = {Fast Optimal Three View Triangulation},
  year         = {2008},
}